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Answer:

Step-by-step explanation:

125x^6 – 8

We write the numbers in exponential form

125= 5*5*5 = 5^3

8 = 2*2*2= 2^3

Now 125x^6 - 8 becomes 5^3x^6 - 3^3

5^3x^2*3- 3^3

We got the expression in cube form a^3- b^3= (a-b)(a^2+ab+b^2)

a= 5x^2  and b= 2

=

The factored form of 125x⁶ - 8 is (5x² - 2)(25x⁴ + 10x² + 4). This expression is obtained by applying the difference of squares formula and then factoring the difference of cubes further.

To factor the expression 125x⁶ - 8, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b).

Step 1: Recognize that 125x⁶ can be expressed as (5x^2)³ and 8 can be expressed as (2)³.

Step 2: Apply the difference of squares formula:

125x⁶ - 8 = (5x²)³ - (2)³

Step 3: Now we have a difference of cubes, so we can factor it as:

125x⁶ - 8 = (5x² - 2)((5x²)² + 5x² * 2 + 2²)

Step 4: Simplify the second part of the expression:

125x⁶ - 8 = (5x² - 2)(25x⁴ + 10x² + 4)

Therefore, the factored form of 125x⁶ - 8 is (5x² - 2)(25x⁴ + 10x² + 4). This expression is obtained by applying the difference of squares formula and then factoring the difference of cubes further.

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Answer:

We know that our world is in 3 dimensions i.e. there are three directions and so, three co-ordinates are required.

Now, if we have to find a position of an object lying on a flat surface, this means that there are only two directions and so, two co-ordinates are needed.

So, we can define the domain ( xy-axis ) in such a way that there are two axis - horizontal where right area have positive values & left area has negative values and vertical where upward side have positive values & downward side has negative values.

For e.g. if we want to find the position of a pen on the table. We will make our own xy-axis and see in which quadrant the pen lies.

Let us say that the pen lies at (2,3), this means that the position of pen is in the first quadrant or it is 2 units to the right of y-axis and 3 units up to the x-axis.

This way we can see that two directions are sufficient to find the position of an object placed on a flat surface.

Final answer:

Position of an object on a flat surface can be adequately described using measurements in the vertical and horizontal directions from a certain reference point. This concept is inherent in the use of vector quantities in physics which allow us to describe motion in two perpendicular directions.

Explanation:

To describe the position of an object on a flat surface, we can use two measures: the vertical and horizontal displacement from a certain reference point. This reference point is often called the origin in a Cartesian coordinate system, which is a type of frame of reference.

Let's imagine you're looking at a map. If we want to specify a location on that map, we can describe it in terms of its distance east (or west) and north (or south) from a particular point. This technique uses horizontal and vertical measurements to describe the position.

This concept is inherent in the idea of vector quantities. In two dimensions, a vector describes motion in two perpendicular directions, such as vertical and horizontal. The principle that motions along perpendicular axes are independent allows us to analyze these two directions separately. Each vector in this context has vertical and horizontal components, and the length of the vector (representing the object's total displacement) is calculated based on these two components.

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Answer:

I know that the equation has infinity many solution

12x+8=12x+8

That would be the final answer

Answer:

of a circle makes 60° angle.

Step-by-step explanation:

There are 360° in one full rotation or we can say that one circle has 360 degrees.

If a circle has 360°, of a circle is equal to

× 360 = 60°

If you divide a circle into  6 equal parts each would be of 60°.

= 60 + 60 + 60 + 60 + 60 + 60 = 360

of a circle makes 60° angle.

The angle that corresponds to 1/6  of a circle is 60 degrees

Which angle corresponds to 1/6 of a circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The distance between any point of the circle and the center is called the radius.

A full circle has an angle 360 degrees. The angle that  corresponds to 1/6 of a circle will be:

1/6 * 360 = 60 degrees

Therefore, the angle that corresponds to 1/6  of a circle is 60 degrees.

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Answer:

quadrant 1

Step-by-step explanation: